(x+1.5)*(x+1.5)=162.25

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Solution for (x+1.5)*(x+1.5)=162.25 equation: 


Simplifying
(x + 1.5)(x + 1.5) = 162.25

Reorder the terms:
(1.5 + x)(x + 1.5) = 162.25

Reorder the terms:
(1.5 + x)(1.5 + x) = 162.25

Multiply (1.5 + x) * (1.5 + x)
(1.5(1.5 + x) + x(1.5 + x)) = 162.25
((1.5 * 1.5 + x * 1.5) + x(1.5 + x)) = 162.25
((2.25 + 1.5x) + x(1.5 + x)) = 162.25
(2.25 + 1.5x + (1.5 * x + x * x)) = 162.25
(2.25 + 1.5x + (1.5x + x2)) = 162.25

Combine like terms: 1.5x + 1.5x = 3x
(2.25 + 3x + x2) = 162.25

Solving
2.25 + 3x + x2 = 162.25

Solving for variable 'x'.

Reorder the terms:
2.25 + -162.25 + 3x + x2 = 162.25 + -162.25

Combine like terms: 2.25 + -162.25 = -160
-160 + 3x + x2 = 162.25 + -162.25

Combine like terms: 162.25 + -162.25 = 0.00
-160 + 3x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '160' to each side of the equation.
-160 + 3x + 160 + x2 = 0.00 + 160

Reorder the terms:
-160 + 160 + 3x + x2 = 0.00 + 160

Combine like terms: -160 + 160 = 0
0 + 3x + x2 = 0.00 + 160
3x + x2 = 0.00 + 160

Combine like terms: 0.00 + 160 = 160
3x + x2 = 160

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 160 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 160 + 2.25

Combine like terms: 160 + 2.25 = 162.25
2.25 + 3x + x2 = 162.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 162.25

Calculate the square root of the right side: 12.737739203

Break this problem into two subproblems by setting 
(x + 1.5) equal to 12.737739203 and -12.737739203.


Subproblem 1
x + 1.5 = 12.737739203

Simplifying
x + 1.5 = 12.737739203

Reorder the terms:
1.5 + x = 12.737739203

Solving
1.5 + x = 12.737739203

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 12.737739203 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 12.737739203 + -1.5
x = 12.737739203 + -1.5

Combine like terms: 12.737739203 + -1.5 = 11.237739203
x = 11.237739203

Simplifying
x = 11.237739203


Subproblem 2
x + 1.5 = -12.737739203

Simplifying
x + 1.5 = -12.737739203

Reorder the terms:
1.5 + x = -12.737739203

Solving
1.5 + x = -12.737739203

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -12.737739203 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -12.737739203 + -1.5
x = -12.737739203 + -1.5

Combine like terms: -12.737739203 + -1.5 = -14.237739203
x = -14.237739203

Simplifying
x = -14.237739203


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.237739203, -14.237739203}

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